SOLUTION: two similar triangles have perimeters of 10" and 30" . the smaller triangle has an area of 4" square what is the area of the larger triangle

Question 951261: two similar triangles have perimeters of 10" and 30" . the smaller triangle has an area of 4" square what is the area of the larger triangle
Found 3 solutions by MathLover1, josgarithmetic, MathTherapy:
Answer by MathLover1(20850)   (Show Source): You can put this solution on YOUR website!

similar triangles have proportional corresponding sides, proportional perimeters, and proportional areas
if two similar triangles have perimeters of and , then

or ratio of similarity is
the smaller triangle has an area of square what is the area of the larger triangle

so,

Answer by josgarithmetic(39620)   (Show Source): You can put this solution on YOUR website!
If right-triangles,

b and h,
and

The bigger triangle,
each length is some factor k times larger than for the small triangle,
and ;
-

The perimeter or second equation tells that k=3; and then the first or area equation tells that .
Answer by MathTherapy(10552)   (Show Source): You can put this solution on YOUR website!

two similar triangles have perimeters of 10" and 30" . the smaller triangle has an area of 4" square what is the area of the larger triangle

Since the similar triangles� perimeters are in a , or ratio, their sides will be in a , or ratio also.
If the sides of similar triangles are in a certain ratio, then their areas will be in the SQUARE of their sides' ratio.
Thus, areas of smaller and larger triangles will be in the ratio of , or
Let area of larger triangle, be A
Then we get:
1(A) = 9(4) --------- Cross-multiplying
A, or area of larger triangle = sq inches
RELATED QUESTIONS
a) The perimeters of two similar triangles are 110 and 65. If the altitude of the smaller (answered by CubeyThePenguin,greenestamps)
Two similar triangles have perimeters of 15 and 8. If the area of the larger triangle is... (answered by checkley77,aplused)
pls. help me to answer: Two similar triangles have perimeters 100 cm and 75 cm. if the... (answered by Theo,josgarithmetic)
The perimeters of two similar triangles is in the ratio 3:4. The sum of their area is... (answered by ikleyn)
Two similar triangles have perimeters of 18cm and 30 cm. Find the ratio of their... (answered by ankor@dixie-net.com)
Two similar triangles have sides in the ratio of 4:5. What is the ratio of their... (answered by venugopalramana)
a) The ratio of similitude of two similar triangles is 3:4. If the perimeter of the... (answered by Boreal)
A square has side length 4x-3n and an equilateral triangle has side length 5x-3. If the... (answered by advanced_Learner)
If the ratio of the lengths of corresponding sides of two similar triangles is 2 : 3, and (answered by Alan3354)