Question

Find the perimeter of a rectangle if its diagonal is 25 cm. and the ragio of length and breadth is 4:3​

Answer 1

Answer:

70cm.

Step-by-step explanation:

Let the length and breadth be 4x and 5x respectively.

As all the angles in a rectangle are right angles, using pythagoras theorem on triangle ABD, we have,

${(ab)}^{2} + ({ad})^{2} = {(bd)}^{2}$

${(4x)}^{2} + {(3x)}^{2} = {25}^{2}$

$16 {x}^{2} + 9 {x}^{2} = 625$

$25 {x}^{2} = 625$

${x}^{2} = 25$

$x = 5$

Length = 4x = 4×5 = 20cm.

Breadth = 3x = 3×5 = 15cm.

Perimeter = 2( length + breadth )

Perimeter = 2 (20+15)

Perimeter = 2×35

Perimeter = 70cm.

Therefore, the perimeter of the rectangle is 70cm.

Hope it helps you.

Good Luck.

Answer 2

Given :-

• Ratio of the length and Breadth = 4 : 3
• Length of diagonal = 25 cm

To find :-

• Perimeter of rectangle

Assumption :-

• Ratio be in x form as 4x and 3x.

Concept :-

• Here the concept of Pythagoras formula will be used.
• We know that All angle of rectangle are 90°. So triangle CBD is right angled triangle because angle C is 90°, BD will be the Hypotenuse , DC is perpendicular and BC is base. So, because of the triangle CBD is right angled triangle.

Here we have :-

• Length = DC = AB = 4x
• Breadth = BC = DA = 3x
• Diagonal = BD = 25 cm

Solution :-

✯ Appling Pythagoras formula to find value of x :-

${ \boxed{ \sf{(Hypotenuse)^2 = (Perpendicular)^2 +( Base)^2 }}}$

${\sf{\implies{(BD)^2 = (DC)^2 +( BC)^2}}}$

${\sf{\implies{(25)^2 = (4x)^2 +( 3x)^2}}}$

${\sf{\implies{625 = 16x^2 +9x^2}}}$

${\sf{\implies{625 = 25x^2}}}$

${\sf{\implies{ \cfrac{625}{25} = x^2}}}$

${\sf{\implies{ x^2 =25 }}}$

${\sf{\implies{ x = \sqrt{25} }}}$

${ \underline{ \boxed{\sf{\implies{ x=5}}}}}$

✯ Putting the value of x in 4x to find Length of Rectangle :-

${ \sf{ \implies{4x}}}$

${ \sf{ \implies{4 \times5 }}}$

${ \underline{ \boxed{ \sf{ \implies{Length = 20 \: cm }}}}}$

✯ Putting the value of x in 3x to find Breadth of Rectangle :-

${\sf{\implies{3x}}}$

${\sf{\implies{3 \times 5}}}$

${\underline{\boxed{\sf{\implies{Breadth = 15 cm}}}}}$

✯ Perimeter of the Rectangle is :-

${\large{\sf{\longmapsto{Perimeter = 2(Length + Breadth)}}}}$

${\large{\sf{\longmapsto{Perimeter = 2(20 + 15)}}}}$

${\large{\sf{\longmapsto{Perimeter = 2(35)}}}}$

${ \underline{ \overline{ \boxed{ \red{\large{\sf{\longmapsto{Perimeter = 70 \: cm \: }}}}}}}}$