Question

Please answer quickly !!! ​

Answer 1

m = 8 is the missing variable.

Explanation:

Given:

Let Name the Triangle First as shown in figure.

∴ Δ AOB ~ Δ BOD

AO = 15

CO = 10

BO = m +4

DO = m

To Find:

m = ?

Solution:

If two triangles are similar then their corresponding sides are proportional, and corresponding angles are equal.

∴ Δ AOB ~ Δ BOD

∴
`(AO)/(CO)= (BO)/(DO)= (AB)/(CD)` {corresponding sides of similar triangle are in proportion}

∴
`(AO)/(CO)= (BO)/(DO)`

Substituting the above given values in it we get

∴
`(15)/(10) =(m+4)/(m) \\15m=10m+40\\15m-10m=40\\5m=40\\m=(40)/(5)\\m= 8`

∴ BO = m +4 = 8 + 4 = 12

∴ DO = m = 8