Question

A boat’s sail is a right triangle. The length of one side of the sail is 7 feet more than the other side. The hypotenuse is 13 feet. Find the lengths of the two sides of the sail.

Answer 1

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Answer 2

The lengths of the two sides of the sail are 5 feet and 12 feet

Step-by-step explanation:

We are given that A boat’s sail is a right triangle.

Let the one side be x

We are given that The length of one side of the sail is 7 feet more than the other side.

Length of other side = x+7

Hypotenuse = 13 feet

Using Pythagoras theorem

$Hypotenuse^2+Perpendicular^2+Base^2\\13^2=x^2+(x+7)^2\\169=x^2+x^2+49+14x\\2x^2+14x-120=0\\x^2+7x-60=0\\x^2+12x-5x-60\\x(x+12)-5(x+12)=0\\(x-5)(x+12)=0\\x=5,-12$

Since the length cannot be negative

Length of other side = x+7=5+7=12

So, The lengths of the two sides of the sail are 5 feet and 12 feet

#Learn more:

The sides forming the right angle of a right-angled triangle are 5cm and 8cm. Find the length of its hypotenuse.

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