FIND THE AREA OF RECTANGLE WITH GIVEN PERIMETER AND DIAGNOL

Question

GOOD MORNING ,

TODAY I'd like to ask a doubt

1. HOW CAN WE FIND THE AREA OF RECTANGLE WITH PERIMETER 68 m AND DIAGNOL 26m ?

Answer 1

draw a rectangle with a diagonal of 26 m

call the width "x" and call the length "y"

2x+2y=68

x+y=34

y=34-x

use the Pythagorean Theorem

x^2+y^2=26^2

x^2+(34-x)^2=26^2

x^2+1156-68x+x^2=676

x^2+1156-68x+x^2-676=0

2x^2-68x+480=0

x^2-34x+240=0

factor or use the quadratic formula

(x-24)(x-10)=0

x-24=0

x=24

x-10=0

x=10

the base and the height of the rectangle are 10 m and 24 m or vice versa

A=l*w

A=10*24

A=240 sq m

Answer 2