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sasho [114]
3 years ago
11

The base of a triangle exceeds its height by 17 inches. if its area is 55 square inches, find the base and height of the triangl

e
Mathematics
1 answer:
Rudiy273 years ago
8 0

<span> </span> <span> Let h = height. This makes the base h + 17.
h(h + 17)/2 = 55
h(h + 17) = 110
h^2 + 17h = 110
h^2 + 17h - 110 = 0
(h + 22)(h - 5) = 0
h = -22 or h = 5
Discard h = -22 because a negative height makes no sense, leaving just
h = 5in
base = 5 + 17 = 22in</span>
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Step-by-step explanation:

If you do not want to read the explanation go the the next part in bold

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This triangle then happens to be a right triangle. ( A triangle formed by a tangent line and a radius is a right triangle.) This means that we can use the Pythagorean theorem to solve for x.

Below here is where the work is shown

a² + b² = c². where a and b = legs and c = hypotenuse. We are given the hypotenuse (5) and a leg (3) So we plug in what we are given and solve for the missing information. 5² = 3² + b²  

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