Math CentralQuandaries & Queries


Question from Josseph, a student:

A right triangle has an area of 84ft sq. and a hypotenuse 25ft long. What are the lengths of the other two sides?


If the length of the two legs of the triangle are L and W then, since the area is 84 square feet

1/2 LW = 84 sq feet so LW = 168 sq feet.

The length of the hypotenuse is 25 feet so what does Pythagoras tell you about L, W and 25?

This gives you two equations in L and W which you can solve for L and W. To solve these equations I used the fact that

(L + W)2 = L2 + 2LW + W2.

Write back if you need more help,

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