Question

the diagnoal of a rectangle is 13 cm and its perimeter is 34cm find its area

Answer 1

Given : Diagonal of a rectangle= 13 cm
Perimeter = 34 cm

To Find : Area of rectangle

Solution :
Let we consider a rectangle ABCD

It's perimeter = 34 cm

AC(Diagonal)=13 cm

Perimeter = 2(L+B)
34 /2=L+B
17=L+B

17-B=L

In ∆ right angle

use pythogorous theorem

AB²+BC²=AC²

B²+L²=13²

B²+(17-B)²=13²

B²+17²+B²-2×17×B=13²

2B²-2×17B=13²-17²

2B²-34B= -120

2B²-34B+120=0

B²-17B+60=0

B²-12B-5B+60

B(B-12)-5(B-12)=0

(B-5)(B-12)=0

B=5,12

Let we take 5 (B<L) assume

L=17-B
L=17-5
L=12

Area of rectangle = l×b
=12×5
=60 cm²