What is BD

Geometry Level 3

$BC$ is parallel to $DE$ .

What is the length of $BD$ In centimeters?

The answer is 5.

2 solutions

Chew-Seong Cheong
May 24, 2017

Since $\triangle ABC$ and $\triangle ADE$ are similar triangles, the height and base length of the triangle are directly proportional any one of the side lengths, therefore, the area of the triangle is directly proportional to the square of the side length. Hence we have:

$\begin{aligned} \frac {[ADE]}{[ABC]} & = \frac {AD^2}{AB^2} \\ \frac {2.34+14.3}{2.34} & = \frac {AD^2}{3^2} \\ \implies AD^2 & = \frac {16.64}{2.34} \times 9 = 64 \\ \implies AD & = 8 \\ \implies BD & = AD-AB = 8 - 3 = \boxed{5} \end{aligned}$

You have not used any units like cm and cm²

Munem Shahriar - 4 years ago

Nope, this is Geometry not Physics. I will use units for Classical Mechanics and Electricity and Magnetism. And units should not appear in equations. I won't also use it in wording a problem because it does not give extra information but lengthen the text of the problem.

Chew-Seong Cheong - 4 years ago

You can check the featured Geometry problems (on the left of the screen) by Brilliant staff. They don't use units other than degree $^\circ$ .

Chew-Seong Cheong - 4 years ago

Munem Shahriar
May 24, 2017

Since BC is parallel to DE, triangles ABC and ADE are similar.

The area of triangle ABC = 2.34 cm²

The area of triangle ADE,

= 2.34 cm² + 14.3 cm²

= 16.64 cm²

Therefore the ratio of the areas of the two triangles

= 2.34 cm² : 16.64 cm²

= 234 : 1664

= 117 : 832

= 9 : 64

= 32 : 82

Then the ratio of the lengths of the two triangles = 3 : 8

or, AD = $\frac{8}{3}$ × AB

= $\frac{8}{3}$ × 3 cm

= 8 cm

BD = 8 cm - 3 cm

= 5 cm (Answer)

What is BD

The answer is 5.

2 solutions

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