Question

The area of rectangle is 56cm square if the measure of its base is by x+5and measurr of height is by x-5 find the dimensions of the rectangle

Answer 1

We know that,

area of a rectangle
= length × breadth
or,
base × height

Given that base = x + 5
height = x - 5
area = 56

So Let us substitute the values,

=> (x + 5)(x - 5) = 56

=> x² - 5² = 56

=> x² - 25 = 56

=> x² = 56 + 25

=> x² = 81

=> x = ± 9

Since we are talking about dimensions, we will always take positive values,
=> x = 9

So base = x + 5 = 9 + 5 = 14 cm
height = x - 5 = 9 - 5 = 4 cm

Hope it helps dear friend ☺️✌️

Answer 2

Hello mate

According to the question given that

The area of rectangle is 56cm²

The base of rectangle is x+5 ......(1)

and hight of rectangle is x-5 ......(2)

Now substitute the given value

$(x + 5)(x - 5) = 56 \\ \\ {x}^{2} - 5x + 5x - 25 = 56$

${x}^{2} = 56 + 25$

${x} {}^{2} = 81 \\ \\ {x} = {9}$

Now, Putting the x value in both equations

x + 5

=> 9 +5

=> 14

so, base of rectangle is 14

x -5

=> 9 - 5

=> 4

so, hight of rectangle is 4

I hope it's help you