Question

Given the two triangles are similar, what are the values of q and t? Round to the nearest hundredth.

Answer 1

Set up proportions. 6/10 = 4.5/t. Cross multiply 6t = 45. Divide both sides of the equation by 6 and get t = 7.5.
Next proportion is q/12.5 = 6/10. Cross multiply 10q = 750. Divide both sides of the equation by 10 and get q = 7,5.

Answer 2

t = 7.5 cm , q= 7.5 cm.

Explanation:

Given : Two similar triangle .

To find : what are the values of q and t ,Round to the nearest hundredth.

Solution : We have given Two similar triangle GHI and DEF.

Property of two similar triangle : The ratios of the lengths of their corresponding sides are equal.

Corresponding sides HI ≅ EF and GI≅DF. GH≅DE

HI = t , EF = 4.5 , GI = 12.5 , DF = q , Gh = 10 , DE = 6

`(t)/(4.5) = (10)/(6)` .

On cross multiplication

t * 6 = 4.5 * 10.

t * 6 = 45 .

On dividing both sides by 6

t = 7.5 cm.

Now, for q

`(q)/(12.5) = (6)/(10)` .

On cross multiplication

q * 10 = 12.5 * 6.

q * 10 = 75.0

On dividing both sides by 10

q= 7.5 cm.

Therefore, t = 7.5 cm , q= 7.5 cm.