Question

Quadrilateral $ABCD$ is a rhombus with perimeter $52$ meters. The length of diagonal $\overline{AC}$ is $24$ meters. What is the area in square meters of rhombus $ABCD?$

$60$

$90$

$105$

$120$

$144$

Video solution:

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Written solution:

We can split the rhombus up into $4$ triangles, each of which looks like this.

We know that this is a right triangle, since the diagonals of a rhombus are perpendicular, and we know the hypotenuse is $52 \div 4 = 13.$

Using the Pythagorean theorem, we get the other leg to be $\sqrt{13^2 - 12^2} = \sqrt{25} = 5.$

This means that the area of the rhombus is $4 \cdot \dfrac{5 \cdot 12}{2} = 4 \cdot 30 = 120.$ Thus, the correct answer is D.

2019 AMC 8 Problem 4

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Problem 4 in Other Years