SOLUTION: A rectangle’s base is 7 cm longer than its height. The rectangle’s area is 144 cm^2? Find this rectangle’s dimensions. You must include units with your answers.

Algebra ->  Rectangles -> SOLUTION: A rectangle’s base is 7 cm longer than its height. The rectangle’s area is 144 cm^2? Find this rectangle’s dimensions. You must include units with your answers.      Log On


   

Question 1137122: A rectangle’s base is 7 cm longer than its height. The rectangle’s area is 144 cm^2? Find this rectangle’s dimensions. You must include units with your answers.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

let rectangle’s base be b and height h
if a rectangle’s base is 7cm longer than its height, we have
b=h%2B7cm........eq.1

if the rectangle’s area is 144cm%5E2, we have
b%2Ah=144cm%5E2...substitute b from eq.1
%28h%2B7cm%29%2Ah=144cm%5E2
h%5E2%2B7cm%2Ah=144cm%5E2
h%5E2%2B7cm%2Ah-144cm%5E2=0....factor completely
h%5E2%2B16cm%2Ah-9cm%2Ah-144cm%5E2=0
%28h%5E2%2B16cm%2Ah%29-%289cm%2Ah%2B144cm%5E2%29=0
h%28h%2B16cm%29-9cm%28h%2B16cm%29=0
%28h+-+9cm%29+%28h+%2B+16cm%29+=+0
solutions: h=9cm or h=-16cm->disregard negative solution or height
so,h=9cm
go to b=h%2B7cm........eq.1, substitute h
b=9cm%2B7cm
b=16cm

answer: rectangle’s base is 16cm and height is 9cm