LogFAQs > #979801772

Pushups strengthen your arms, chest, and upper back.

Planks are a great core exercise and you can benefit from them (or any ab exercise) besides just "having abs." Having a strong core will make you appear thinner, improve your posture and balance, and lower your chances of spinal injury.

Infinite number of benefits from pushups as well. "I don't plan on being thin" is a terrible reason to not do them, or any exercise.

Edit: I typed my post when there were still no other posts ITT, and I gotta say I'm proud of CE for having so many reasonable responses this quickly. CE is more health conscious than one might assume.