Everything Is Proportional

Geometry Level 1

The area of two similar triangles is ${169\text{ cm}^2 }$ and ${121\text{ cm}^2}$ respectively. The length of the longest side of the larger triangle is $26\text{ cm}$ . Find the length of the longest side of the smaller triangle.

11\text{ cm}

18\text{ cm}

22\text{ cm}

24\text{ cm}

1 solution

Yash Jain
Mar 30, 2016

When 2 triangles are similar then the ratio of their areas equals the square of the ratio of their corresponding sides.

Let the length of the longest side of the smaller triangle be $x$ .

$\frac{169}{121} = (\frac{26}{x})^2$

$x^2 = \frac{21 \times 26 \times 26}{169}$

$x \Rightarrow \boxed{22}$ .

Yep! Thanks for the solution! Upvoted!!

Skanda Prasad - 5 years, 2 months ago

Well I did differently : the area of a triangle is equal to 1/2basexheigh so for the bigger triangle we have 26/2xh = 169, 13h = 169, h = 169/13, h = 13, h = 1/2b, The smaller triangle is similar so h = 1/2b is also true for this one So 1/2bxh = hxh, So hxh = 121, So h = square root of 121, h = 11, h = 1/2b, So b = 2h, b = 2x11, b = 22,

Sorry for my english I'm french and I'm not used to speak about science yet, also my solution is longer but as long as it works it's ok I guess

Jérémy Reignoux II - 5 years ago

It's ok, bro! Doesn't matter... Nice solution, anyway...

Skanda Prasad - 5 years ago

Everything Is Proportional

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