Question

The area of a rectangle one of whose sides is 5cm. and diagonal 13cm. is

Answer 1

let  breadth be 5cm

diagonal=13cm

then by pgt

13sq=bsq+5sq

169-25=bsq

b=√144

b=√12sq

b=12cm

now area l*b

12*5=60cmsq

thnx might be its wrong i tried my best dear

Answer 2

Answer:

Area of rectangle = 60 cm²

Step-by-step explanation:

Given:

Let the given side be breadth, b

b = 5 cm

diagonal = 13 cm

length, l = ?

Consider the rectangle ABCD given below,

BC = 5 cm

AC =13 cm

Here, we can see that ΔABC is a right-angled triangle formed here,

Using Pythagoras theorem,

hypotenuse² = base² + altitude²

⇒ AC² = AB² + BC²

⇒ 13² = AB² + 5²

⇒ AB² = 13² - 5²

⇒ AB² = 169 - 25

⇒ AB² = 144

⇒ AB = $\sqrt{144}$

⇒ AB = 12

We got, the length of the rectangle = 12 cm

∴ Area of rectangle = length × breadth

                                = AB × BC

                                = 12 × 5

                                = 60 cm²

Pythagoras theorem:

In a right-angled triangle, the sum of squares of legs of the triangle is equal to the square of hypotenuse of the triangle.

i.e., hypotenuse² = base² + altitude²

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