The diagonal of a rectangle is 8 m longer than its shorter side. If the area of the rectangle is 60 square m, find its dimensions.

Question

The area of the rectangle was 60 square meters. Its diagonal has 8 meters longer than its shorter side. Find its dimensions.

 

Answer 1

Hi Xierylle,

 

Suppose side of rectangle= width= w m

     so diangonal of a rectangle= (w+8) m

      Length of a rectangle= l m

Area of a rectangle= l * w = 60 sq m,  ....w= 60/l  .....eq 1 

For rectangle, all angles are right angles, using pythagoras theorem,                  or we can use ( 5:12:13)

 

l² + w² = (w+8)²

l² + w² =w² +16w +64

l² = 16w+64, now from eq 1,

 

l²= 16(60/l) +64

l²-960/l -64 =0

l³-64l-960=0

l³ -12l² +12l² -144l +80l -960 =0

l²(l-12) +12l( l-12) +80(l-12) =0

l-12 =0

l=12

w=60/l=60/12=5

 

dimensions are 12m & 5 m