Math, asked by Tarzan6300, 7 months ago

Sum of length and breadth e is 14 Area is 48 find diagonal

Answers

Answered by Anonymous
28

let x and y be the sides of the rectangle.

Then the area is xy = 48

By Pythagoras’s theorem, x^2 + y^2 = 10^2 = 100

Then (x + y)^2 = x^2 + y^2 + 2xy = 100 + 2*48 = 196

So the perimeter is 2(x + y) = 2 sqrt(196) = 28

&lt;html&gt;</p><p>&lt;head&gt;</p><p>&lt;style&gt;</p><p>h1{</p><p>text-transform:uppercase;</p><p>margin-top:90px;</p><p>text-align:center;</p><p>font-family:Courier new,monospace;</p><p>border:3px solid rgb(60,45,8);</p><p>border-top:none;</p><p>width:67%;</p><p>letter-spacing:-6px;</p><p>box-sizing:border-box;</p><p>padding-right:5px;</p><p>border-radius:6px;</p><p>font-size:35px;</p><p>font-weight:bold;</p><p>}</p><p>h1 span{</p><p>position:relative;</p><p>display:inline-block;</p><p>margin-right:3px;</p><p>}</p><p>@keyframes shahir{</p><p>0%</p><p>{</p><p>transform: translateY(0px) rotate(0deg);</p><p>}</p><p>40%</p><p>{</p><p>transform: translateY(0px) rotate(0deg);</p><p>}</p><p>50%</p><p>{</p><p>transform: translateY(-50px)rotate(180deg);;</p><p>}</p><p>60%</p><p>{</p><p>transform: translateY(0px)rotate(360deg);;</p><p>}</p><p>100%</p><p>{</p><p>transform: translate(0px)rotate(360deg);;</p><p>}}</p><p>h1 span</p><p>{</p><p>animation: shahir 3s alternate infinite linear;</p><p>}</p><p>h1 span:nth-child(1)</p><p>{color:pink;</p><p>animation-delay: 0s;</p><p>}</p><p>h1 span:nth-child(2)</p><p>{color:lightmaroon;</p><p>animation-delay: 0.2s;</p><p>}</p><p>h1 span:nth-child(3)</p><p>{color:red;</p><p>animation-delay:0s;</p><p>}</p><p>h1 span:nth-child(4)</p><p>{color:lightgreen;</p><p>animation-delay: 0.4s;</p><p>}</p><p>h1 span:nth-child(5)</p><p>{color:blue;</p><p>animation-delay: 0.5s;</p><p>}</p><p>h1 span:nth-child(6)</p><p>{color:purple;</p><p>animation-delay: 0.3s;</p><p>}</p><p>&lt;/style&gt;</p><p>&lt;meta name="viewport" content="width=device-width" &gt;</p><p>&lt;/head&gt;</p><p>&lt;body&gt;</p><p>&lt;center&gt;</p><p>&lt;div&gt;</p><p>&lt;h1&gt;</p><p>&lt;span&gt;D&lt;/span&gt;</p><p>&lt;span&gt;i&lt;/span&gt;</p><p>&lt;span&gt;v&lt;/span&gt;</p><p>&lt;span&gt;y&lt;/span&gt;</p><p>&lt;span&gt;a&lt;/span&gt;</p><p>&lt;span&gt; 2&lt;/span&gt;</p><p>&lt;span&gt;5&lt;/span&gt;</p><p>&lt;span&gt;1&lt;/span&gt;</p><p>&lt;span&gt;2&lt;/span&gt;</p><p>&lt;span&gt;5&lt;/span&gt;</p><p></p><p>&lt;/h1&gt;</p><p>&lt;/div&gt;</p><p>&lt;/center&gt;</p><p>&lt;/body&gt;</p><p>&lt;/html&gt;</p><p>

Answered by Anonymous
16

\huge\mathfrak\blue{Answer:}

Given:

  • We have been given rectangle whose area is 48cm²
  • Sum of length and breadth of rectangle is 48cm²

To Find:

  • We have to find the measure of diagonal of the given rectangle

Solution:

Let the length of rectangle = x

Breadth of rectangle = y

According to the Question

\implies x + y = 14

\implies y = ( 14 - x ) _______( 1 )

_________________________________

Also we have

\implies Area = 48 cm²

\implies (Length) x (Breadth) = 48 cm²

\implies xy = 48 cm²

Putting value of y from equation ( 1 )

\implies x ( 14 - x ) = 48

\implies 14x - x² = 48

\implies x² - 14x + 48 = 0

Solving the Equation using Middle Term Splitting Method

\implies x² - 8x - 6x + 48 = 0

\implies x ( x - 8 ) - 6 ( x - 8 ) = 0

\implies ( x - 8 ) ( x - 6 ) = 0

Hence Either x = 8 or x = 6

_______________________________

\huge\mathfrak\red{Case1:}

\fbox{When x = 8}

\implies y = 14 - x

\implies y = 14 - 8

\implies \fbox{y = 6}

\huge\mathfrak\red{Case2:}

\fbox{When x = 6}

\implies y = 14 - 6

\implies \fbox{ y = 8}

_______________________________

Either x = 8 and y = 6 or Vice Versa

Let the Diagonal of rectangle = D cm

Using Pythagoras Theorm

\implies ( D )² = ( x )² + ( y )²

\implies D² = ( 8 )² + ( 6 )²

\implies D² = 64 + 36

\implies D² = 100

Taking square root on both sides

\implies D = \sqrt{100}

\implies \fbox{D = 10 cm}

Diagonal of Rectangle is 10 cm

________________________________

\huge\mathfrak\red{Verification:}

\fbox{Sum = 8 + 6 = 14 cm}

\fbox{Area = 8 \times 6 = 48 }

Hence Verified !!

Previous Question
Next Question
Similar questions
Math, 3 months ago
(2-y²)(5+y²) answer please...
English, 3 months ago
I will tell you the Newton's 4 th law--- A hole always attract a pole the length of pole is equal to the depth of hole when a pole is in motion it's always produce lotion. - Albert Nitin​​ ​...
Math, 3 months ago
52 points plzzz answer​...
Chemistry, 7 months ago
see the pic and tell me the answer plzz Ques- Take some copper sulphate in a beaker and add some water to it. 1. What is the colour of the solution so formed? 2. Now add a piece of iron to it and allow it to stand for few hours. What do you observe? 3. Why has the colour changed? 4. What conclusion do you draw? 5. Give a chemical equation for the reaction.​
Physics, 7 months ago
pls tell these answer​...
Math, 10 months ago
the base of an isosceles triangle is 18cm and it's area is 108cm².Find it's perimeter​...
English, 10 months ago
For all ______, the test is over a) intensive porpoises b) intents and purposes c) intensive purposes...
Math, 10 months ago
9. Find the missing letters in the following additions ABT + 895 113A ​...