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SSAT Middle Level
Quantitative (Math)

Area of Triangle from Side Ratios

Very Hard Geometry And Measurement Triangles And Polygons

In triangle XYZ, the lengths of sides XY, YZ, and XZ are in the ratio of 3:4:5. If the perimeter of triangle XYZ is 48 cm, determine the area of the triangle.

Recall that the area of a triangle can be computed using the formula: $$Area = \frac{1}{2} \times base \times height$$ or by using Heron's formula: $$Area = \sqrt{s(s-a)(s-b)(s-c)$$, where $s$ is the semi-perimeter, and $a$, $b$, and $c$ are the lengths of the sides.

Hint

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