Question

Base of triangle exceeds the height by 4. If the area is 178.5 square inches, find the length of the base and the height of the triangle

Answer 1

Area of a triangle:
A= (1/2)(bh)

In this problem we are given:
A= 178.5 $in^{2}$
b= h+4 in
h= UNKNOWN ("h")

Plug in our values into the area equation and solve for "h":
$A= \frac{1}{2} bh$
$178.5 = \frac{1}{2} ((h+4)h)$ (multiply each side by 2 to get rid of the 1/2)
$357 = ((h+4)h)$
$357 = h^{2} +4h$
$0= h^{2} +4h -357$
(357/21=17)
$0= (h+21)(h-17)$ (solve both inequalities separately)

$0= (h+21)$
$-21= h$ ( a negative height is not possible so, this answer is incorrect.)

$0=(h-17)$
$h=17 in$

Answer: base = (h+4)= (17+ 4) b= 21 in h= 17in


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