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July 10th, 2018, 10:27 AM   #1
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Sides of a triangle using ratios and area

Hello, I have a question that I cannot find the solution to and would be grateful for any help.

A right-angled triangle has an area of 2.8m^2. The sides are in the ratio of 5:12:13 and the triangle stands on the shortest side.
Calculate the following:
a) the perpendicular height
b) the hypotenuse

again thank you for any help.

Last edited by skipjack; July 10th, 2018 at 10:53 AM.
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July 10th, 2018, 10:53 AM   #2
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Originally Posted by Jamtrehope View Post
Hello, I have a question that I cannot find the solution to and would be grateful for any help.

A right-angled triangle has an area of 2.8m^2. The sides are in the ratio of 5:12:13 and the triangle stands on the shortest side.
Calculate the following:
a) the perpendicular height
b) the hypotenuse

again thank you for any help.
You first need to know the formula for area of a triangle: $\displaystyle A = \frac{1}{2} b h$. Now you need an expression for the actual triangle sides. They are all in a ratio "x". Then b = 5x and h = 12x. Thus we know that
$\displaystyle 2.8 = \frac{1}{2} (5x)(12x)$

Solve this for x and then you can say what b = 5x and h = 12x are.

Can you finish?

-Dan
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Last edited by skipjack; July 10th, 2018 at 10:59 AM.
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July 10th, 2018, 10:57 AM   #3
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If the "perpendicular height" is 12y, the other sides have lengths 5y and 13y. What is the triangle's area in terms of y? Oh, topsquark posted much the same while I was typing!
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July 10th, 2018, 11:19 AM   #4
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Thank you for your quick response. I can sleep easy now.

Last edited by skipjack; July 10th, 2018 at 11:48 AM.
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