Question
Triangle ABC is similar to triangle DEF. For triangle
ABC, sides are AB = 6 cm, BC = 8 cm, CA = 10 cm. If DE corresponds to AB and DE = 9 cm, find the lengths of EF and FD and the area of triangle DEF.Solution
Scale factor (DEF to ABC): k = DE / AB = 9 / 6 = 3/2 So: EF corresponds to BC ⇒ EF = k × BC = (3/2) × 8 = 12 cm FD corresponds to CA ⇒ FD = k × CA = (3/2) × 10 = 15 cm Area of triangle ABC: Right-angled at B (6-8-10 triangle): Area(ABC) = (1/2) × 6 × 8 = 24 cm² Area scales with square of linear factor: Area(DEF) = k² × Area(ABC) = (3/2)² × 24 = (9/4) × 24 = 54 cm²
The ratio of the sums invested by ‘X’ and ‘Y’ in SIP ‘M’ and ‘N’ is 7:4, respectively. If ‘X’ invested Rs. 6300 more than ‘Y’, t...
If certain sum of amount becomes Rs. 9024 in 12 years and Rs. 13536 in 24 years at a certain rate of compound interest, compounded annually then find th...
- The total amount received on a certain sum of money at the rate of interest of 15% per annum compound interest after 3 years is Rs. 36501. What was the pri...
- Anil borrowed Rs. 7,200 at simple interest of 15% p.a. and Rs. 8,400 at simple interest of 12% p.a. The total interest he paid after ‘y’ years is Rs. 8...
Rajat invested Rs. (P-100) on compound interest at the rate of ‘R’ % per annum compounded annually. Ravi invested Rs. (P+300) on simple interest at ...
A certain sum becomes triple in 8 years at simple interest. Find the rate of interest.
If the ratio of the sum invested and simple interest received after 1 year is 25:16 respectively, then find the rate of interest.
After how many years, Rs. 4400 will become 5324 at the rate of 10% p.a., compounded annually?
A certain amount becomes four times itself when invested at r% per annum simple interest for 12 years. What is the value of r?
A certain sum of money invested at a rate of 48% p.a. amounts to Rs. 20736 at the end of 15 months if the rate of interest is compounded 5 monthly. Find...
