Question

If BC = 6 and AD = 5, find DC. 4 4.5 7.2

Answer 1

Answer:

The length of CD is 4 units

Step-by-step explanation:

Given the triangle ABC and if BC = 6 units and AD = 5 units

we have to find the length of DC.

In ΔABC and ΔBDC

∠ABC=∠BDC    (each 90°)

BC=BC   (common)

∠C=∠C   (Common)

By ASA rule, ΔABC≈ΔBDC

Therefore their corresponding sides are in proportion

$\frac{BC}{AC}=\frac{BD}{AB}=\frac{CD}{BC}$

$\frac{BC}{AC}=\frac{CD}{BC}$

Let CD=x units

$BC^2=(AC)(CD)$

$6^2=(AD+CD)CD$

$36=(5+x)x$

$36=5x+x^2$

$x^2+5x-36=0$

$x^2+9x-4x-36=0$

$x(x+9)-4(x+9)=0$

$(x-4)(x+9)=0$

x=4, -9

Distance can't be negative therefore

The length of CD is 4 units