Question

1. Given that the scale factor of two similar triangles is 4:5, and the perimeter of the smaller triangle is 30cm, find the perimeter of the bigger triangle?

2. The perimeter of two similar triangles are 13.2 cm and 25.8cm. If one side of the smaller triangle measures 3.5 cm, how long is its corresponding sides in the bigger triangle?

3. Suppose the perimeters of two similar triangles are 14 cm and 72 cm. If the altitude of the smaller triangle is 4 cm, how long its corresponding altitude in the bigger triangle?

4.The sum of the perimeters of two similar triangles is 20 m. If a pair of corresponding sides of the triangle is of length 3m and 4m, What is the perimeter of the smaller triangle?

5. The sun of the areas of two similar triangles is 70m2. If the a pair of corresponding sides of the triangles is of length 4m and 3m, What is the area of the smaller triangle?

7.The corresponding sides of two similar triangles ABC and XYZ are 8cm and 10cm if one altitude of *triangleshape
ABC is 6cm how long is the corresponding altitude *triangle shape XYZ?

8.If the areas of two similar triangles are 125cm2 and 169cm2, Find the ratio of any pair of corresponding sides the?

9. The length of the corresponding sides of two similar triangles are 32cm and 160cm. If the area of the larger triangle is 1600cm2, what is the area of the smaller triangle?

Answer 1

Answer:

the question is so long write the small question how can we anwer it

Answer 2

Answer:

1. 37.5cm

2. 6.841cm

3. 20.571cm

4. 8.571m

5. 25.2m^2

7. 7.5cm

8. 1.163

9. 64cm^2

Step-by-step explanation:

1. Let sides of triangle are a,b,c ; then sides of corresponding similar triangle will be $\frac{5a}{4} ,\frac{5b}{4} and \frac{5c}{4} .$

parimeter of smaller triangle = a+b+c = 30 cm.  ............(1)

perimeter of bigger triangle = 5/4(a+b+c)= 30*5/4=37.5cm.

2. Let $x,y$ and $z$ be the side of smaller triangle then sides corressponds to its simmilar triangle would be $kx,ky$ and $kz$. $(k > 1)$

given that Perimeter of smaller triangle is 13.2, $\implies x+y+z=13.2...(1)$,

and perimeter of bigger triangle is 25.8$\implies k(x+y+z)=25.8..........(2)$

Dividing equation (1) and (2) we get $k \approx 1.955.$ So side corresponding to 3.5 will be $k$ times $\implies 3.5*1.955 \approx 6.841$cm.

3. Simmilarly $k = \frac{72}{14} \approx 5.143.$ Corresponding altitude $\implies 4*5.143 \approx 20.571$cm

4. Given,$(k+1)(x+y+z)= 20.......(1)$

Corresponding sides of two simmilar triangle are 3m and 4m$\implies k= 4/3.$

Putting value of $k$ in eq.(1) we get $\frac{7(x+y+z)}{3} =20 \implies x+y+z\approx 8.571m$(perimeter of smaller traingle).

5. Area of triangle from Heron's formula is given by

$A_{1} = \sqrt{s(s-x)(s-y)(s-z)} ......(1)$

Corresponding are of simmilar traingle whose sides are k times of sides of smaller triangle is given by$A_{2} = \sqrt{ks(ks-kx)(ks-ky)(ks-kz)} =k^{2} \sqrt{s(s-x)(s-y)(s-z)} ........(2)$

given that

$(k^{2} +1)\sqrt{s(s-x)(s-y)(s-z)} = 70m^{2}$ and $k = 4/3.$

so,$\sqrt{s(s-x)(s-y)(s-z)} = 25.2 m^{2}$

7.. $k= 10/8.$ Length of corresponding altitude is 6*5/4 =7.5cm

8.Given that

$\frac{k^{2} \sqrt{s(s-x)(s-y)(s-z)}}{ \sqrt{s(s-x)(s-y)(s-z)}} =\frac{169}{125} \implies k \approx1.163$

9. Given k = 160/32 = 5. and $k^{2} \sqrt{s(s-x)(s-y)(s-z)}=1600cm^2 \implies A_1 =1600/5^2 = 64cm^2$