SOLUTION: please help me solve this question:-ABCD is a rectangle in which AB=(4x+3)cm and BC=(3x-2)cm. PQR is a triangle in which PQ=5xcm QR=4x cm and PQR=90degree the area of rectangle

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Question 234099: please help me solve this question:-ABCD is a rectangle in which AB=(4x+3)cm and BC=(3x-2)cm.
PQR is a triangle in which PQ=5xcm QR=4x cm and PQR=90degree
the area of rectangle ABCD is equal to the area of the triangle PQR
(i)form an equation in x and show that it reduces to 2x square+x-6=0
(ii)solve the equation to find the value of x
(iii)find the length of PQ
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the rectangle is:
A%5Br%5D+=+%284x%2B3%29%283x-2%29
A%5Br%5D+=+12x%5E2%2Bx-6
The area of the triangle is:
A%5Bt%5D+=+%281%2F2%29%284x%29%285x%29
A%5Bt%5D+=+10x%5E2
A%5Br%5D+=+A%5Bt%5D so...
12x%5E2%2Bx-6+=+10x%5E2 Subtract10x%5E2 from both sides.
highlight%282x%5E2%2Bx-6+=+0%29 Solve by factoring.
%282x-3%29%28x%2B2%29+=0
2x-3+=+0 or x%2B2+=+0 so that...
x+=+3%2F2 or x+=+-2 Discard the negative solution as lengths are positive.
highlight%28x+=+3%2F2%29
PQ+=+5x
PQ+=+5%283%2F2%29
highlight%28PQ+=+7.5%29cm.